The generalized retraction methods in fixed point theory for nonself operators
type: Item
instance of: scholarly article
zbMATH Open document ID: 1326.47067
author: Ioan A. Rus
publication date: 2014-10-27T00:00:00Z
full work available at URL: http://www.math.ubbcluj.ro/~nodeacj/download.php
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 54H25
Mathematics Subject Classification ID: 54C15
zbMATH DE Number: 6361933
zbMATH Keywords: fixed point
zbMATH Keywords: retraction
zbMATH Keywords: nonself operator
zbMATH Keywords: contractive operator
MaRDI profile type: Publication
title: The generalized retraction methods in fixed point theory for nonself operators
published in: Fixed Point Theory
review text: In this work, the author proposes an approach to some well-known fixed point results under mild contractive conditions (Caristi-Kirk theorem, Jachymski theorem, etc.)\ through the so-called generalized retraction methods.NEWLINENEWLINEA~mapping \(f: Y\to X\), where \(Y\subseteq X\) and \(X\) carries some structure with it, is called retractable with respect to the retraction \(\rho: X\to Y\) if the fixed point set of \(f\) coincides with that of the composition \(\rho\circ f\). Several results are obtained out of the classical ones by adding the condition that the nonself operator \(f\) is retractable for a certain retraction.
reviewed by: Rafa Espínola
description: scientific article; zbMATH DE number 6361933